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Education quality and returns to schooling: evidence from migrants in Brazil

We provide a new education quality index for states within a developing country using 2010 Brazilian data. This measure is constructed based on the notion that the financial returns obtained from an additional year of schooling can be
seen as being derived from the value that market forces assign to this education. We use migrant data to estimate returns to schooling of individuals who studied in different states but who work in the same labor market. We find very heterogeneous educational qualities across states: the poorest Brazilian region presents education quality levels that are approximately equal to one-third of the average of all other regions, a gap three times larger than the one suggested by standardized test scores. We compare our index with standardized test scores, educational outcome variables, and public expenditure per schooling stage at the state level, producing new evidence related to education in a large developing country. We conduct an education quality-adjusted development accounting exercise for Brazilian states and find that human capital accounts for 26%-31% of output per worker differences. Adjusting for quality increases human capital’s explanatory power by 60%.

3.
Education Quality and Returns to Schooling:
Evidence from Migrants in Brazil
Luiz Mário Brotherhood Pedro Cavalcanti Ferreira Cezar Santos
Escola Brasileira de Economia e Finanças (EPGE/FGV)
February 4, 2017
Abstract
We provide a new education quality index for states within a developing coun-
try using 2010 Brazilian data. This measure is constructed based on the notion
that the ﬁnancial returns obtained from an additional year of schooling can be
seen as being derived from the value that market forces assign to this education.
We use migrant data to estimate returns to schooling of individuals who stud-
ied in diﬀerent states but who work in the same labor market. We ﬁnd very
heterogeneous educational qualities across states: the poorest Brazilian region
presents education quality levels that are approximately equal to one-third of the
average of all other regions, a gap three times larger than the one suggested by
standardized test scores. We compare our index with standardized test scores,
educational outcome variables, and public expenditure per schooling stage at the
state level, producing new evidence related to education in a large developing
country. We conduct an education quality-adjusted development accounting ex-
ercise for Brazilian states and ﬁnd that human capital accounts for 26%-31% of
output per worker diﬀerences. Adjusting for quality increases human capital’s
explanatory power by 60%.
Keywords: education quality, returns to schooling, development accounting.
JEL Classiﬁcation: I21, I25, I26.
1 Introduction
Education is very important for socioeconomic development.1
A country’s level of edu-
cation has two dimensions: quantity and quality. The ﬁrst dimension has been studied
extensively,2
but the same is not true for quality. This dimension is very complex
because it may involve subjective considerations, making it very hard to measure. Nev-
ertheless, some authors argue that quality of education matters more than quantity for
1
See Sen (2000) and Banerjee and Duﬂo (2012).
2
For reviews of this literature, see Sianesi and van Reenen (2003) and Krueger and Lindahl (2000).
1

4.
economic growth. For example, Hanushek and Wobmann (2007) point out that sev-
eral studies found that including education quality variables in development accounting
exercises can reduce years of schooling’s explanatory power, leaving it mostly insigniﬁ-
cant.
In this paper we provide a new education quality index for states within a country
using 2010 Brazilian data. This measure is constructed based on the notion that the
ﬁnancial returns obtained from an additional year of schooling can be seen as being
derived from the value that the market assigns to this education. Therefore, diﬀerences
between returns to schooling of individuals who studied in diﬀerent states, all else equal,
are due to diﬀerences between the quality of the educational services that they have
consumed.
At ﬁrst, one might think of constructing such measures by computing educational
returns for each state independently. However, a possible drawback of this approach
is that two distinct labor markets may reward the same education quality diﬀerently.
For example, suppose that skilled labor is scarce in low-income states, implying that
educational returns are higher than in high-income states. Imagine that an individual is
considering whether to go to college in a given region. This individual’s college premium
will be higher in low-income states and lower in high-income states, even though the
quality of her education is the same in both cases. Thus, interpreting educational
returns in diﬀerent labor markets as education quality measures may lead to biased
analysis.
To prevent this type of bias, we use data on individuals who obtained their education
in diﬀerent states but who work in markets with similar characteristics. This is accom-
plished by using 2010 census data on individuals living at the time in São Paulo, the
largest Brazilian state in terms of population and GDP. The 2010 census contains infor-
mation on migration that can be used to infer which migrants likely completed schooling
in their state of birth, which allows us to select only individuals who ﬁt our criteria.
This strategy is the same as the one used in Schoellman (2012). Since migrants may
be positively self-selected,3
we also use Heckman’s (1979) selection correction method.
Brazil has ﬁve geographic regions,4
which are very unequal in terms of economic
outcomes. The Northeast and North are the country’s poorest regions, with per capita
GDP in 2013 equal to R$ 12,954 and R$ 17,213 respectively, followed by the South
(R$ 30,495), Midwest (R$ 32,322), and Southeast (R$ 34,789). Compatible with this
ranking, our method produces very heterogeneous educational quality indexes across
states. Regional means range from 3.4% in the Northeast to 9.7% in the Southeast.5
We compare education qualities across both Brazilian states and the world, and ﬁnd
that the two distributions are quite similar.
3
See Ferreira and Santos (2007).
4
For the distribution of Brazilian states across geographic regions, see Table B4 in the appendix.
5
We do not consider the North region because our dataset contains an insuﬃcient number of
observations of migrants in São Paulo who were born in northern states.
2

5.
After constructing this state-level quality measure, we investigate its association
with other educational variables. First, we compare our educational quality measure
with standardized test scores, and conclude that there are important diﬀerences and
similarities between them. On the one hand, our method depicts a more unequal sce-
nario than test scores do: northeastern states’ mean education quality is equal to 90%
of the other regions’ aggregate mean in the case of test scores, but only 30% in the case
of our index. This is evidence that there are aspects related to education quality that
our method captures, but test scores do not. On the other hand, despite this diﬀerence
there is a strong association between both indexes: an increase of one standard devia-
tion in standardized test scores is associated with an increase of 2.5 percentage points
in returns to schooling. Second, we ﬁnd a very strong association between educational
quality, school attendance, and the mean age-grade gap.6
Third, we investigate the rela-
tionship between educational quality measures and public investments on education by
schooling stage. We conclude that higher educational quality is signiﬁcantly associated
with higher public expenditures on primary education, but insigniﬁcantly related to
higher expenditures on secondary or tertiary education. We interpret this as suggestive
evidence that public investments in earlier stages of education are more eﬀective than
those in later stages, in accordance with the literature discussed in Heckman (2006).
The high correlation between our index, standardized test scores, and educational
outcome variables is evidence that supports the use of returns to education as an educa-
tional quality measure. For some developing and underdeveloped countries, education
quality variables are scarce, whereas data on earnings and schooling are readily avail-
able. Therefore, verifying the correlation between returns to schooling, test scores,
and educational outcome variables can support researchers interested in constructing
education quality measures for developing and underdeveloped countries.
Some authors corroborate that returns to schooling of immigrants are positively
correlated with mean educational quality in the source state/country. Using 1980 U.S.
census data, Card and Krueger (1992) ﬁnd that men who were educated in states with
higher-quality schools have a higher return on additional years of education. Chiswick
and Miller (2010) and Bratsberg and Terrell (2002) verify that international test scores
explain diﬀerences in the rate of return to schooling among immigrants in the United
States. Li and Sweetman (2013) conclude the same for the case of Canada. We con-
tribute to this literature by documenting a signiﬁcant association between returns to
schooling of cross-state migrants and educational variables in the home state in a large
developing country.
Using our education quality measure, we conduct a development accounting exercise
for Brazilian states. We ﬁnd that quality-adjusted human capital accounts for 26%-31%
of output per worker diﬀerences in Brazil, while non–quality-adjusted human capital
explains 17.5% of GDP per worker variability. All told, taking education quality into
6
The age-grade gap is the diﬀerence between the expected and actual age of a student attending
a given grade.
3

6.
account increases human capital’s explanatory power by 60%, implying that this is
an important component to consider if one is interested in understanding economic
development within regions of a country. Those ﬁndings are consistent with the human
capital data constructed in Figueiredo and Nakabashi (2016), which imply that human
capital accounts for 27% of output per worker variability across Brazilian states. Our
results are also quantitatively similar to recent quality-adjusted development accounting
studies conducted for U.S. states (Hanushek et al., 2015), and to recent cross-country
exercises (Schoellman, 2012).
This paper is organized in ﬁve additional sections. Section 2 describes the datasets,
the sample selection strategy, and presents descriptive statistics. Section 3 explains the
method used to construct educational quality measures and analyzes the results. Sec-
tion 4 compares our education quality index with other educational variables. Section 5
conducts development accounting exercises for Brazilian states using a quality-adjusted
human capital variable. Section 6 presents concluding comments.
2 Data and sample selection
In order to estimate educational returns, we use data from the 2010 Brazilian census.
This dataset is provided by the Instituto Brasileiro de Geograﬁa e Estatística7
(IBGE),
and contains information related to individuals’ residence characteristics, work, migra-
tion, schooling, mobility, and fertility. We use data on individuals’ earnings from their
main job, hours worked per week, schooling attainment, age, state of birth, state of
residence, race, gender, and urban/rural residence.
Our ﬁrst objective is to select a sample of individuals who work in labor markets
with similar characteristics, but who obtained education in diﬀerent states. This is
accomplished by using data on individuals who work in São Paulo, the largest Brazilian
state in terms of population and GDP. However, the 2010 census does not provide direct
information on where an individual’s schooling was obtained. We follow the same
strategy as in Schoellman (2012) and use information on age and year of migration
to infer which migrants likely completed schooling in their state of birth. Therefore,
our baseline sample only includes migrants who arrived in São Paulo after completing
24 years, e.g., six years past the expected high school graduation date. This six-year
buﬀer is used in order to minimize measurement error that may result from migrants
who repeat grades, start school late, or experience interruptions in their education. We
exclude migrants who are studying in São Paulo and, for individuals who were born
and work in São Paulo, we exclude those who are studying in another state or those
who previously lived in another state. We exclude individuals who are younger than 24
or older than 65.
The 2010 census also lacks information on the exact number of years of schooling
7
Brazilian Institute of Geography and Statistics.
4

7.
attainment for each individual. Instead, it is possible to construct a categorical educa-
tional variable that identiﬁes the following intervals for years of schooling: from 0 to
3 years, 4–7, 8–10, 11–14, and 15 years or more. We deal with this limitation in two
alternative ways. First, we impute individuals’ years of schooling in the ﬁrst four inter-
vals as the interval midpoint, and use 15 years for individuals in the last interval. This
imputation strategy is the same as the one used with U.S. census data in Hendricks
(2002) and Schoellman (2012). Second, in Appendix A we estimate returns to school-
ing using dummy variables for each educational category and calculate the weighted
mean return using the fraction of individuals in each interval as weights. Both methods
produce qualitatively similar results.
Table B4 in the appendix contains descriptive statistics and the number of observa-
tions by state of birth. Our baseline sample includes individuals who do not live in São
Paulo because those observations are used in Heckman’s selection correction method.
We exclude the North region and Distrito Federal in our main analysis because they
present an insuﬃcient number of observations of migrants – including those observations
produces estimates with large standard errors, making inference questionable.
To compare our education quality measures with other educational variables, we
use data on standardized test scores, educational outcome variables, and public expen-
diture by schooling stage. For standardized test scores, we use Sistema Nacional de
Avaliação da Educação Básica8
(Saeb) test scores for the year 1995. The Saeb exam
is administered by the Instituto Nacional de Estudos e Pesquisas Educacionais Anísio
Teixeira9
(Inep), an institution associated with the Ministry of Education. Since 1995,
this exam has been composed of biennial mathematics and Portuguese tests applied to
samples of students in primary and secondary education in public and private schools.
For educational outcome variables, we use 1991 data provided by IPEADATA (2016)
on 7- to 14-year-old students’ mean school attendance and 10- to 14-year-old students’
mean age-grade gap. We also use Abrahão and Fernandes’ (1999) data on public expen-
ditures on education per student by schooling stage (primary, secondary, and tertiary
education) in 1995.
3 Returns to schooling as educational quality mea-
sures
Our objective is to construct a new measure of the quality of educational services by
state in Brazil through the estimation of returns to schooling. Our strategy builds on
Schoellman’s (2012) idea that the ﬁnancial returns obtained from an additional year
of schooling can be seen as being derived from the value that the market assigns to
this education. Therefore, diﬀerences between returns to schooling of individuals who
8
National System of Basic Education Evaluation.
9
Anísio Teixeira National Institute for Research on Education.
5

8.
studied in diﬀerent states, all else equal, is due to diﬀerences between the quality of
educational services that they consumed.
A ﬁrst approach to implement this idea empirically is to independently estimate the
following augmented Mincerian regression for each state:
log(Wi) = α + βSi + γXi + ui, (1)
where i indexes the individual; W denotes earnings per weekly hours worked; S denotes
years of schooling; X is a vector of control variables that includes gender, age, age
squared, race, and urban residence dummy; and u is an error term. β is the return to
schooling.
The ﬁrst column of Table 1 displays returns to schooling estimates obtained by
separately estimating equation (1) for each state. In this speciﬁcation the northeastern
region, one of the poorest in Brazil, presents the highest returns. For example, one
additional year of schooling in Piauí is associated with a 10% increase in earnings.
Santa Catarina, from the rich southern region, has the lowest return, equal to 6.5%.
Interpreting these estimates as educational quality measures is problematic because
labor market characteristics vary signiﬁcantly across Brazilian states, making it possible
that two diﬀerent markets could reward the same schooling quality diﬀerently. To
overcome this problem, we use data only on individuals who work in São Paulo, but
who obtained education in diﬀerent states. We estimate the following speciﬁcation:
log(Wij) = αj + βjSij + γXij + uij, (2)
where j indexes individual i’s state of birth. αj is a state-of-birth ﬁxed eﬀect, and βj
is the return to schooling for individuals who studied in state j.
The second column of Table 1 provides returns to schooling estimates using only
individuals who work in São Paulo in our baseline sample. For comparison with the
previous result, Figure 1a plots estimates of the ﬁrst two models. Note that the two
methods produce very diﬀerent estimates. For example, Northeastern states’ estimates
are the largest in Model 1, but are the smallest in Model 2. Rio de Janeiro (RJ),
Espírito Santo (ES), Rio Grande do Sul (RS), and Santa Catarina (SC) also have very
divergent estimates. This result is consistent with the idea that skilled labor is scarce
in lower income states, so that market forces oﬀer a high reward for education in those
regions. Once we use data only on individuals who work in the same labor market,
we are able to obtain an improved measure of education quality as valued by market
forces.
However, the estimates from Model 2 may still be questionable if we want to interpret
returns as educational quality measures. If migrants are positively self-selected, São
Paulo’s return to schooling might be underestimated because it is obtained using only
non-migrant data. Formally, earnings in São Paulo are obviously not observed for
6

10.
Figure 1: Comparison of educational returns estimates between models
(a) Models 1 and 2
MA
PI
CERN
PB
PE AL
SE
BA
MSMT
GO
PR
SC RS
MG
ES
RJ
SP
.04.06.08.1.12.14
Model2
.06 .07 .08 .09 .1
Model 1
45 degree line
(b) Model 2 and Heckit
MA
PI
CERN
PB
PEALSE
BA
MSMT
GO
PR
SCRS
MG
ES
RJ
SP
.04.06.08.1.12
HeckitModel
.04 .06 .08 .1 .12 .14
Model 2
45 degree line
Geographic regions are identiﬁed by diﬀerent markers: Northeast , Midwest , South , and South-
east .
individuals who do not work there. If the decision to work in São Paulo is determined
by variables that are correlated to individuals’ years of schooling, estimation of (2) by
OLS produces biased and inconsistent estimates. Therefore, we use Heckman’s (1979)
selection correction method (the Heckit Model) and postulate that individuals work in
São Paulo if
δj + ηSij + φZij + ψEij + vij > 0, (3)
where δj are intercepts that vary across states of birth; Z contains the same variables
as X, except for the urban residence dummy; Eij is the (expected) earnings per hour of
individual i if she decides to work in São Paulo in relation to working in another state;
and v is an error term. Speciﬁcally, for an individual working in São Paulo, Eij is equal
to her earnings divided by her expected earnings if she were to work in another state.
For an individual working in a state other than São Paulo, Eij equals the expected
earnings if she was to work in São Paulo divided by her actual current earnings. To
calculate expected earnings we use ﬁtted values of linear regressions. That is, we ﬁrst
run a series of regressions of earnings per weekly hours on years of schooling, gender,
age, age squared, race, and the urban residence dummy for each possible combination
of state of birth and a dummy variable that indicates residence in São Paulo. Then, for
example, the expected earnings for working in São Paulo for an individual who studied
in Rio de Janeiro is computed as the ﬁtted value of the regression that uses data on
individuals who work in São Paulo and were born in Rio de Janeiro. Additionally, we
8

11.
Figure 2: Heckit estimates and 95% conﬁdence intervals
Piauí
Paraíba
Maranhão
Bahia
Pernambuco
Ceará
Alagoas
Rio Grande do Norte
Sergipe
Paraná
Mato Grosso do Sul
Mato Grosso
Minas Gerais
Goiás
São Paulo
Espírito Santo
Santa Catarina
Rio Grande do Sul
Rio de Janeiro
0 .05 .1 .15
Northeast
Midwest
South
Southeast
posit that
uij ∼ N(0, σ2
), vij ∼ N(0, 1), corr(uij, vij) = ρ. (4)
This is our baseline speciﬁcation, which we estimate through the Maximum Like-
lihood method. For comparison, Figure 1b plots estimates of Model 2 and Heckit.
Observe that all states have lower estimates in Heckman’s model, except for São Paulo.
This is evidence that migrants are positively selected and that the Heckit model corrects
the selection bias by increasing São Paulo’s returns in relation to the other states.
The third column of Table 1 and Figure 2 display returns to schooling estimates
that can be interpreted as educational quality measures. Rio de Janeiro and Piauí
present the highest and lowest estimates, respectively. That is, after controlling for
migration selection issues, if we take two individuals who have studied in Rio de Janeiro,
work in São Paulo, and display the same observable characteristics, except for the fact
that one individual has one more year of schooling than the other, it is expected that
the earnings of the more educated individual are 13.1% higher than the other’s. In
contrast, one additional year of education in Piauí, one of the poorest states in Brazil,
increases earnings by only 2.3%. The Northeast region unambiguously presents the
lowest educational quality, while the other regions display some heterogeneity. Mean
educational returns by region are: Northeast 3.4%, Midwest 6.9%, South 8.9%, and
9

12.
Figure 3: Education quality within Brazil and across countries
(a) Distributions0.511.5
Kerneldensity
0 .2 .4 .6 .8 1
Education quality
Brazil
World
(b) Quantile-quantile plot
1
2 3 45 6 789
101112
13
1415
16 17 18
19
0.2.4.6.81
Brazil
0 .2 .4 .6 .8 1
World
Quantile
45 degree line
Education quality at country level is given by returns to schooling estimated in Schoellman (2012).
Southeast 9.7%.10
There are important similarities and diﬀerences between our education quality index
and the education quality measures across countries worldwide produced in Schoellman
(2012). First, education quality in Brazil ranges from 2.3% (Piauí) to 13% (Rio de
Janeiro), whereas across the world it ranges from approximately zero (Tonga and Al-
bania) to 12% (Switzerland and Tanzania). For reference, Figure 3a plots education
quality distributions within Brazil and across countries, after normalizing the largest
value of each to one. Instead of arbitrarily selecting numbers in the education quality
interval, however, a more appropriate method for comparing the two distributions is
to investigate their quantiles. Figure 3b displays the quantile-quantile plot for the two
distributions. Each dot represents a quantile, out of nineteen, for each distribution.
Since we are working with nineteen states in Brazil, each state corresponds to a dif-
ferent quantile. The ﬁrst nine quantiles of the Brazilian distribution correspond to the
northeastern states. We can divide the quantiles of both distributions in four subsets:
(i) the ﬁrst three quantiles, (ii) the fourth to the sixth, (iii) the seventh to the ninth, and
(iv) the last ten. The dots in the ﬁrst set lie above the 45 degree line, meaning that the
northeastern states with the lowest education qualities have higher relative quality than
10
Heckman et al. (1996) revisit the literature’s results on the association between education quality
and returns to schooling for the U.S. and ﬁnd that measured schooling quality only aﬀects the returns
for college graduates. We investigate if this is also the case for Brazil by re-estimating our baseline
speciﬁcation, dropping observations for college graduates. The correlation between returns to schooling
for the complete sample and this subsample is equal to 0.95. Therefore, our estimates are not driven
by the returns for college graduates.
10

13.
Table 2: Heckit selection equation elasticities
Elasticity Standard error
Years of schooling 0.0453 0.0012
Earnings ratio 0.0312 0.0072
Age -0.0098 0.0001
Race
Black 0.1428 0.0041
Pardo 0.1459 0.0025
Other 0.1792 0.0095
Woman -0.0086 0.0020
All estimates are signiﬁcant at one percent. Elasticities in terms of the following variations. Years of
schooling and Earnings ratio: one standard deviation increase centered in the mean value. Age: from
35 to 36 years. “Pardo” is a term used by the IBGE that broadly encompasses multiracial Brazilians.
the corresponding countries in the lowest quantiles. The dots in the second set lie close
to the 45 degree line, implying that both distributions are similar in this segment. In
the third set, the opposite of that observed in set (i) happens. These properties found
in sets (i) and (iii) almost perfectly oﬀset each other, so that the Northeast’s mean
position in the Brazilian distribution is equivalent to the mean position of countries in
the same quantiles in the worldwide distribution. In fact, education quality means in
the ﬁrst nine quantiles of both distributions are not statistically diﬀerent. In set (iv),
the distributions behave very similarly to each other because the dots lie very close to
the 45 degree line. Therefore, we conclude that both distributions are quite similar.
Consistent with this, the Gini coeﬃcients for both distributions are very close and not
statistically diﬀerent: 0.25 for Brazil and 0.27 across the world.
Table 2 shows elasticities related to the coeﬃcients in the selection equation (3). A
one standard deviation increase in schooling (expected earnings derived from working
in São Paulo in relation to other states) produces a 4.5% (3.2%) higher probability
of working in São Paulo. An individual who is 36 years old presents a 0.9% lower
probability of working in São Paulo than an individual who is 35.
The correlation between the error terms estimate is ˆρ = 0.7, and the p-value asso-
ciated with the test ρ = 0 is approximately equal to zero. Therefore, we reject the null
and conclude that there is selection bias in the estimates from Models 1 and 2.
4 Education quality and other educational variables
In this section we investigate the association between our educational quality measures
and standardized test scores, schooling outcomes, and public expenditure on education
per schooling stage.
To study standardized test scores, we use data on the 1995 Saeb exams. To make an
11

14.
Figure 4: Returns to schooling and Saeb test scores
AL
BA
CE
MA
PB
PE
PI
RN
SE
GO
MS
PR
RS
SC MG
RJ
SP
0.05.1
Returnstoschooling
-2 -1 0 1 2
Saeb test scores (std)
beta: 0.025
se: 0.006
p: 0.000
R2: 0.573
corr: 0.757
The solid line and all values in the box, with the exception of “corr,” are related to the OLS estimation
between the variables. “corr” denotes correlation coeﬃcient. “std” denotes standardized variable. Ge-
ographic regions are identiﬁed by diﬀerent markers: Northeast , Midwest , South , and Southeast
.
adequate comparison in terms of timing, we re-estimate educational returns using the
subsample of individuals who were probably studying when the exams were applied,
which amounts to selecting individuals between 24 and 32 years of age. Table B5
displays descriptive statistics for this young subsample. Note that there are states
for which there is a very small number of migrants in São Paulo, making educational
returns’ standard errors very large for those cases. Because of this we exclude states for
which there are less than 100 migrants; as a result, Espírito Santo and Mato Grosso are
not included in this analysis. Tables B2 and B3 display returns to schooling estimates
and selection equation elasticities for this sample. The correlation between the full and
young sample educational returns is 0.95.
Figure 4 displays returns to schooling and standardized Saeb test scores, along with
some correlation statistics. The two measures are highly correlated: the correlation
coeﬃcient equals 0.75, and a one standard deviation increase in Saeb test scores is
associated with an increase in returns to schooling of 2.5 percentage points. However,
there are signiﬁcant diﬀerences between both indexes: the Northeast region’s mean
Saeb score is equal to 90% of the others regions’ mean. In the case of our educational
quality index, this number equals 30%. The Gini coeﬃcients associated with Saeb and
our measure are equal to 0.03 and 0.34, respectively. That is, our measure suggests a
larger discrepancy between regions’ educational qualities than the Saeb scores do. If we
think of our index as the value that market forces assign to education, this is evidence
that there are educational components that the market captures, but test scores do not.
12

15.
Figure 5: Returns to schooling and educational outcomes
AL
BA
CE
MA
PB
PE
PI
RN
SE
GO
MS
PR
RS
SC
MG
RJ
SP
-101
Schoolattendance(std)
-1 0 1 2
Returns to schooling (std)
beta: 0.868
se: 0.128
p: 0.000
R2: 0.753
corr: 0.868
ALBA CEMA PB
PE
PI
RN
SE
GO
MS
PR
RSSC
MG
RJ
SP
-1.5-1-.50.51
Age-gradegap(std)
-1 0 1 2
Returns to schooling (std)
beta: -0.860
se: 0.132
p: 0.000
R2: 0.740
corr: -0.860
The solid line and all values in the box, with the exception of “corr,” are related to the OLS estimation
between the variables. “corr” denotes correlation coeﬃcient. “std” denotes standardized variable. Ge-
ographic regions are identiﬁed by diﬀerent markers: Northeast , Midwest , South , and Southeast
.
Next, we investigate the association between our educational quality measures and
schooling outcomes at the state level. We use 1991 data on 7- to 14-year-old students’
mean school attendance and 10- to 14-year-old students’ mean age-grade gap by state.
To make a compatible comparison, we again use schooling returns estimates obtained
using the subsample of young workers. Figure 5 displays correlation statistics between
education quality and (i) mean school attendance and (ii) the age-grade gap. Note
the signiﬁcant association between the variables: a one standard deviation increase in
returns to schooling is associated with a 0.9 standard deviation increase in mean school
attendance and a 0.88 standard deviation decrease in the age-grade gap. The high
R-squared value also implies that linearity is a good approximation for the relationship
between returns to schooling and the educational outcome variables.
The strong association between educational returns and standardized test scores,
mean school attendance, and the age-grade gap is evidence that returns to schooling
can be used as a proxy variable for educational quality in cases where the latter is not
available. Since the use of proxy variables in regressions relies on linearity assump-
tions, the evidence for a linear relationship between educational outcome variables and
returns to schooling supports this conclusion. For some developing and underdevel-
oped countries, educational quality measures are scarce, whereas data on earnings and
schooling are readily available. Therefore, verifying the correlation between returns to
schooling, test scores, and educational outcomes is relevant for researchers interested
in investigating education themes in developing and underdeveloped countries through
13

16.
the construction of education quality measures.
Next, we assess the relationship between educational quality and government ex-
penditure on education per student for diﬀerent schooling stages in 1995. Since the
greatest part of students enrolled in primary, secondary, and tertiary education in 1995
were aged 7 to 25, and therefore were 22 to 40 in 2010, we use educational returns
estimates obtained using the full sample of workers in 2010. Figure 6 exhibits cor-
relation measures between the two variables. First, the association is positive for all
schooling stages. However, it is signiﬁcant only for public investments in primary edu-
cation. In fact, the OLS coeﬃcient associated with primary education is greater than
the secondary and tertiary education coeﬃcients at 2% and 7% signiﬁcance levels. The
coeﬃcient associated with secondary education is not signiﬁcantly diﬀerent from the
tertiary education coeﬃcient. This is suggestive evidence that public investments in
earlier stages of education are more eﬀective than in later stages, in accordance with
the literature discussed in Heckman (2006).
14

18.
5 Development accounting
In this section we conduct a development accounting exercise for Brazilian states. To
estimate human capital stocks, we follow Schoellman (2012) and parametrize the human
capital production function of state j as
h(Sj, Qj) = exp
(SjQj)η
η
, (5)
where Sj and Qj denote state j’s mean years of schooling and education quality, re-
spectively, and η is an elasticity parameter. We have data on Sj and have produced
education quality measures in Section 3. To estimate the production function param-
eter, we use Schoellman’s (2012) equilibrium model, which generates a relationship
between observable variables that can be used to estimate η.
The equilibrium model features very standard components. Households are com-
posed by dynasties. A dynasty is a sequence of workers who are altruistically linked in
the sense of Barro (1974). Each worker lives for a ﬁnite number of periods, then dies
and is replaced by a young worker who inherits his assets but not his human capital.
Workers are endowed with one unit of time each period to allocate between school and
work. There is a competitive ﬁrm that hires labor and rents capital to maximize proﬁts.
Education quality is exogenous.
The optimal decisions of workers and ﬁrms generate the following equilibrium rela-
tionship between quantity of schooling, quality of education, and returns to education,
Mj:
log(Sj) =
η
1 − η
log(Qj) −
1
1 − η
log(Mj). (6)
In our context, Mj are the returns to education for non-migrants.
Table 3 displays estimates of the elasticity of years of schooling with respect to ed-
ucation quality, η/(1 − η), using the speciﬁcation given by equation (6). The rows also
contain the implied value of η and the number of observations used in the regressions.
São Paulo is not included in the estimation sample because QSP ≡ MSP . We use two
Table 3: Estimated elasticity of years of schooling with respect to education quality
OLS IV
Unweighted Weighted Unweighted Weighted
Elasticity 0.18 0.25 0.20 0.26
(0.08) (0.07) (0.09) (0.07)
Implied η 0.15 0.20 0.16 0.21
N 17 17 17 17
Standard errors in parentheses.
16

19.
diﬀerent estimation methods: constrained OLS and constrained IV. In the latter, we in-
strument education quality using 1995 Saeb test scores because returns to education for
immigrants may be measured with some error due to small sample sizes (Schoellman,
2012). We ﬁnd that OLS estimates are close to IV estimates, suggesting that measure-
ment error is not a signiﬁcant issue. We also test a speciﬁcation where we weight each
state observation by the number of immigrants in the sample. In general, the elasticity
estimates range between 0.18 and 0.26, which implies that η is between 0.15 and 0.21.
These estimates are close to those produced in a robustness exercise in Schoellman
(2012), where ˆη = 0.21. This result is found when one uses Bils and Klenow’s (2000)
data on non-migrants’ returns to schooling in order to allow for variability in Mj, in a
way similar to our usage here.
Using equations (5) and (6), human capital in equilibrium can be written as
log(hj) =
MjSj
η
. (7)
This equation is directly comparable to the one used by the development account-
ing literature that does not account for quality-adjusted years of schooling (Bils and
Klenow, 2000), given by
log(hj) = MjSj. (8)
We use equations (7) and (8) to construct quality-adjusted and non–quality-adjusted
years of schooling for Brazilian states. Note that the right hand side of these equations
diﬀer by a quality markup factor of 1/η, which implies that quality-adjusted log human
capital stocks are 4.7-6.6 times larger than non–quality-adjusted stocks.
Since Mincerian returns are noisy, we follow a strategy similar to the one adopted
in Bils and Klenow (2000) and Schoellman (2012), and use the trend relationship be-
tween schooling and returns to schooling of non-migrants rather than individual state
observations in order to compute human capital stocks in (7) and (8). The estimated
relationship is
log(Mj) = b1 + b2 log(Sj) = −0.68 − 0.80 log(Sj), (9)
with standard errors of 0.78 and 0.36.
The ﬁrst two columns of Table 4 display our development accounting results. The
ﬁrst row presents one estimate of the fraction of output per worker diﬀerences that
is accounted for by quality-adjusted years of schooling, obtained by comparing the
variance of log human capital to the variance of log output per worker. Using this
metric, human capital accounts for 6%-12% of output per worker diﬀerences. According
to Caselli (2005), although this measure is nicely grounded in the tradition of variance
decomposition, it has the drawback that variances are sensitive to outliers. A measure
that is less sensitive to outliers is the inter-percentile diﬀerential, obtained by comparing
the human capital ratio of the 90th and 10th percentiles to the output per worker ratio
of the 90th and 10th percentiles. By this metric, human capital accounts for 44%-
17

20.
Table 4: Development accounting results
Quality-adjusted Not quality-
η = 0.15 η = 0.21 adjusted
var[log(h)]
var[log(y)]
0.128 0.065 0.003
h90/h10
y90/y10
0.505 0.448 0.353
50% of output per worker diﬀerences. To conservatively summarize our results, we
compute the mean between the two measures and conclude that quality-adjusted years
of schooling account for about 26%-31% of output per worker diﬀerences in Brazil.11
The third column in Table 4 shows that using non–quality-adjusted human capital
stocks would imply that years of schooling account for about 17.5% of output per worker
diﬀerences, about 60% of the explanatory power obtained previously. This is evidence
that education quality is a very important component to consider if one is interested in
studying education in Brazil.
Figueiredo and Nakabashi (2016) construct two quality-adjusted human capital vari-
ables for Brazilian states using 2000 data. The ﬁrst variable relies on Ideb test scores,12
and the second one is based on each state’s mean expected earnings, conditional on
the education and experience levels of the working-age population. Our ﬁndings are
consistent with the results produced through the second variable, which imply that the
ratio between the variances of log human capital and output per worker is equal to 0.05,
while the inter-percentile diﬀerential equals 0.5.13
Hanushek et al. (2015) use achieve-
ment scores adjusted for selective migration to produce human capital stocks for U.S.
states, ﬁnding that 20%-35% of per-capita GDP variation can be explained by human
capital. In terms of cross-country development accounting literature, our results are
also quantitatively similar to those found by Schoellman (2012), whose baseline results
suggest that quality-adjusted years of schooling account for 21%-26% of output per
worker diﬀerences.
11
The ﬁndings in Hendricks (2002) are similar to ours in the sense that the variance decomposition
and inter-percentile diﬀerential measures produce qualitatively distinct results, equal to 0.07 and 0.22,
respectively.
12
Índice de Desenvolvimento da Educação Básica (Ideb) is an educational quality index developed
by Inep, and embodies Saeb test scores and approval rates. We do not consider Ideb in this paper
because it is available only from 2005, a relatively recent year. Our dataset contains information on
individuals who were working in 2010, and most of them studied many years before 2005.
13
Figueiredo and Nakabashi’s (2016) human capital variable produced through Ideb test scores
displays very large variability, generating variance and percentile ratios equal to 0.37 and 0.72.
18

21.
6 Conclusion
In this paper we provide a new measure of education quality for Brazilian states in
2010, based on the idea that the ﬁnancial returns obtained from an additional year
of schooling can be seen as being derived from the value that the market assigns to
this education. We use census data on migrants in the state of São Paulo in order to
estimate returns to schooling of individuals who obtained education in diﬀerent states,
but who work in the same labor market.
We ﬁnd that educational quality is very heterogeneous across states, following the
large economic inequality in Brazil. In fact, our index implies that education quality
is more unequal across states than standardized test scores imply. This is a relevant
result for the debate on educational quality in Brazil, suggesting that there are educa-
tional aspects that market forces capture, but standardized test scores do not. Further
research is warranted in order to disentangle which elements each method considers.
We document a strong correlation between our education quality measures and stan-
dardized test scores and educational outcome variables, supporting the use of returns
to education as an educational quality index.
We ﬁnd that higher educational quality is signiﬁcantly associated with greater public
expenditure on primary education at the state level, but insigniﬁcantly related to higher
public expenditure on secondary or tertiary education. This is suggestive evidence that
public investments in earlier stages of education are more eﬀective than in later stages,
in accordance with the literature discussed in Heckman (2006). However, the Brazilian
government’s expenditure per student in tertiary education in 2008 was equal to 1.17 of
OECD countries’ mean expenditures. For the case of secondary and primary education,
these proportions were equal to 0.22 and 0.30 (OECD, 2011). Our results reinforce the
pool of stylized facts that motivate rethinking the Brazilian government’s education
investment proﬁle.
Finally, we conduct education quality-adjusted development accounting exercises for
Brazilian states and conclude that human capital plays an important role in explaining
output per worker diﬀerences. Ignoring education quality reduces human capital’s ex-
planatory power by 40%, suggesting that this is an important component to consider if
one is interested in understanding economic development within regions of a country.
References
J. Abrahão and M. A. C. Fernandes. Sistema de informações sobre os gastos públicos
da Área de educação – SIGPE: Diagnóstico para 1995. Texto para Discussão 674,
IPEA, 1999.
A. Banerjee and E. Duﬂo. Poor Economics: A Radical Rethinking of the Way to Fight
Global Poverty. PublicAﬀairs, 2012.
19

24.
Appendix
A Categorical schooling variable
In Section 3 we used imputed schooling data because the 2010 census does not provide
the exact number of individuals’ years of schooling. An alternative to this imputation
is using a categorical schooling variable that identiﬁes the following years of schooling
intervals: from 0 to 3 years, 4–7, 8–10, 11–14, and 15 years or more. We proceed in
two steps. First we estimate Heckman’s model, modifying equation (2) to
log(Wij) = αj +
5
k=1
βjkDijk + γXij + uij, (10)
where k assumes the 5 possible values of the categorical schooling variable and Dijk
is a dummy that indicates if individual i’s schooling belongs to interval k. We also
use the categorical schooling variable in the selection equation (3). This step produces
4 schooling coeﬃcients for each state (one of them is omitted to avoid collinearity).
Second, we compute for each state the weighted mean of schooling coeﬃcients using
the fraction of individuals in each schooling interval as weights. The result is an average
of marginal eﬀects for each state.
Figure A1 plots Heckman’s model estimates using imputed and categorical schooling
variables. Both methods produce qualitatively similar results. Note that averages
of marginal eﬀects have diﬀerent magnitudes than the educational returns estimated
previously. This happens because those estimates no longer have the interpretation of
an expected increase in earnings due to one additional year of schooling.
Figure A2 and Table A1 display returns estimates. Conﬁdence intervals are signiﬁ-
cantly larger in this case because we estimate 160 additional parameters. Besides this,
standard errors increase when we compute the weighted average of marginal eﬀects.
22